Propagation network of tailings dam failure risk and the identification of key hazards

The tailings dam system is complex, and the dam structure changes continuously over time, which can make it difficult to identify key hazards of failure and characterize the accident formation process. To solve the above problems, based on complex network theory, the paper uses the identified hazards and the relationship between hazards to construct the propagation network of tailings dam failure risk (PNTDFR). The traditional analysis methods of network centrality usually focus on one aspect of the information of the network, while it cannot take into account to absorb the advantages of different methods, resulting in the difference between identified key nodes and real key hazards. To find the key hazards of tailing dam failure, based on the characteristics of multi-stage propagation of failure risk, the paper proposes a multi-stage collaborative hazard remediation method (MCHRM) to determine the importance of hazard nodes by absorbing the advantages of different centrality methods under different hazard remediation (deletion) ratios. The paper applies the above methods to Feijão Dam I. It can be found that when the priority remediation range is increased to 45%, the key hazards obtained by the MCHRM will cover all the causes of accidents proposed by the Dam I failure investigation expert group. Besides, the paper compares the monitoring data, daily inspection results and safety evaluation information of key hazards with the ‘Grading standards of hazard indicators’, and obtains the formation process of the Dam I failure and 30 key hazards in trigger state.

www.nature.com/scientificreports/ hazards can only cause other hazards and cannot be caused by other hazards. The in-degree value of dormant hazards is 0, including all initial nodes of the four influencing factors of tailings dam failure, such as floods, excessive rainfall, and excessive standard earthquakes. Armed hazards are formed by the evolution of the dormant hazards or other armed hazards, and these armed hazards will may cause damage accidents under certain working environments or conditions, such as the rapid rise of pond water level, the dam deformation, and the tailings liquefaction. These hazards mean the imminent accidents and disasters. Active hazards are accidents that are or have occurred. If these active hazards cannot be effectively suppressed, they will lead to serious consequences and disasters, including overtopping and dam break and so on 24 . When the network model is established, we can use complex network theory to analyze the statistical features of the PNTDFR, such as degree, betweenness centrality, network density, characteristic path length and clustering coefficient. From these characteristics, the propagation law of tailings dam failure risk can be analyzed and discovered.
Analysis of key hazard nodes. When the PNTDFR is a scale-free network, the PNTDFR will appear vulnerable to deliberate attacks 34 . In other words, if we can prioritize to remedy the hazard nodes that have a greater impact on network connectivity, the propagation efficiency of the network can be reduced, thereby slowing down or even blocking the propagation of risks. Therefore, the paper chooses network efficiency as an index to measure the spreading ability of dam-break risk.
Global network efficiency, also known as network connectivity, refers to the difficulty of average network connectivity, which is the average of the sum of the reciprocal lengths of the shortest path between all pairs of hazard nodes in the entire network 34 . Degree centrality, betweenness centrality and closeness centrality are commonly used methods to characterize the importance of nodes in complex networks. In this paper, the importance of hazard nodes determined by the three methods is used as the priority of hazard remediation (node deletion), and then the differences of the three methods in reducing network efficiency are compared. By absorbing the advantages of different methods under different hazard remediation ratios, combined with the characteristics of multi-stage propagation of tailings dam failure risk, this paper proposes a multi-stage collaborative hazard remediation method (MCHRM) to determine the importance of hazard nodes. The specific implementation process of this method is as follows: (1) Since the first-layer nodes (dormant hazards) only have out-degree values, and the betweenness centrality is 0, only the degree value needs to be considered in determining the remediation order of the first-layer hazards, and priority is given to the hazard nodes with greater degree value. (2) The second-layer nodes (armed hazards) have degree values, betweenness centrality and closeness centrality, which are in the intermediate stage between the dormant hazard and the activity hazard. Therefore, it is necessary to consider the influence of three indicators on risk propagation at the same time. When there are differences among three hazard remediation methods under different remediation proportions, priority is given to the remediation method that can reduce the speed of risk evolution faster. (3) The third-layer nodes (activity hazards) are the possible accident modes of a tailings dam, and the remediation method is the same as that of the second-layer node. The hazard of dam break is the object of the accident studied in this paper, so it is not remedied. (4) After the remediation priority of hazards at the same layer according to the corresponding methods is determined, those nodes with a smaller remediation proportion will be prioritized among hazard nodes at different layers.
When all the hazard nodes of the PNTDFR have been treated, by observing the change trend of network efficiency, the key hazard nodes of the PNTDFR can be determined (those nodes that can significantly reduce network efficiency after deleting). In this paper, these important nodes are called key hazards in failure accident. In addition, if the MCHRM can reduce network efficiency more effectively than the commonly used methods in the past, the remediation (deletion) order of hazards (nodes) determined by the MCHRM can better characterize the importance of hazards in the dam failure accident. Accident formation process. If you want to determine which of the hazards caused an accident, you need to determine whether these hazards are in a triggered state and how serious. Because the China Tailings Pond Safety Grade Classification Standard divides the tailings ponds into four levels: normal, mild, moderate, and dangerous, the paper also divides the grading standards of the key hazard indicators of tailings dams into four levels combining the Technical Regulations for Safety of Tailings Pond and the Code for Design of Tailings Facilities. Level 1 is a normal state, level 2 is a mild danger, level 3 is a moderate danger, and level 4 is a serious danger. In the classification of grading standards, the indicators that can obtain specific values are classified using quantitative analysis methods. For example, the evaluation indicator of hazard 5 (Heavy rainfall) is rainfall, which is calculated in the depth of the water layer per unit area within 24 h. Hazards that are difficult to quantitatively classify are qualitatively used. For example, hazard 355 (Insufficient experience in personnel or organization qualification problems) are divided into four levels based on the personnel's education, working hours, and qualification levels of the institution. According to the above method, the paper has formulated the grading standards of some hazard indicators, as shown in "Appendix B".
When the classification standard of the key hazard is completed, by comparing the monitoring data, daily inspection results, and safety evaluation information before the accident, the levels of the key hazards in the studied tailings dam can be obtained, so as to determine the states of these hazards 35  www.nature.com/scientificreports/ that causes the tailings dam to break. The remaining hazards with a level greater than 1 are the key hazards that led to the dam failure. By excluding the hazard nodes of level 1, we can determine the key hazards and evolution paths between hazards. In the accident investigation report, these key hazards are also referred to as the main cause of the accident.

Case analysis
The Identification of hazards and the relationship between Hazards. A total of 117 hazards and 535 relationships are obtained by the THIF method, as shown in "Appendix A" 32 . In "Appendix A", the first column indicates the categories of hazards, including four categories: environment factor, personnel factor, material factor, and management factor. The second column indicates the number (ID) of the hazards in the third column. The fourth column indicates the number of the hazards caused by the hazard in the third column. For example, the hazard named 'heavy rainfall' in the second row of the third column is numbered 5, which belongs to the environment factor. Through the THIF method, we can get the hazards that may be caused by the 'heavy rainfall' . These hazards are numbered 19, 67, 69, 150, 193 and 19. Propagation network of Dam I failure risk. This section uses hazards of Dam I and the relationship between the hazards in "Appendix A" to construct the adjacency matrix, and then import it into Pajek software to construct the propagation network of Dam I failure risk (I-FRPN), as shown in Fig. 1.
Degree and degree distribution. The degree value of each node in I-FRPN can be obtained through Pajek complex network software as shown in Fig. 2. The average degree of the I-FRPN is 9.15, and the network density is 0.04, indicating that a hazard node is directly related to 9.15 hazard nodes on average, but the overall density of the I-FRPN is not large. It can be seen from Fig. 2 that among the top 10 hazards, 355 (Insufficient experience in personnel or organization qualification problems) is the hazard node with the largest degree value in the I-FRPN, which directly affects 61 hazards. It shows that if the personnel and organization do not have sufficient experience or do not meet the corresponding qualification requirements, the tailings dam will always be threatened throughout its life cycle. 191 (Fracture of drainage structure) is directly related to 36 hazards, which is the second largest hazard in the degree value. It is classified as a material factor among the four influencing factors.  www.nature.com/scientificreports/ with the hazard 191, and account for 70% of the top 10 hazards, highlighting the fact that the material factor plays a leading role in tailings dam safety management. Hazard 308 (Closure design not in accordance with regulations) has a degree value of 25, which belongs to the same personnel factor as hazard 355, and these hazards are indirect factors that lead to dam break. 351 (Improper maintenance) is directly related to 24 hazards, which is the management factor, indicating that management plays an important role in the safety management of tailings dams.
From the point of view of out degree, the values of hazards 355 (Insufficient experience in personnel or organization qualification problems), 308 (Closure design not in accordance with regulations), 351 (Improper maintenance), 2 (Flood) and 312 (Dam body remediation does not meet the requirements) are respectively 61, 24, 23, 19, and 16, which are the five nodes with the largest out-degree value, indicating that personnel factors, management factors, and environmental factors are more likely to cause other hazards. 191 (fracture of drainage structure), 62 (partial landslide and collapse of dam), 64 (dam instability), 65 (dam deformation), and 157 (failure of water filter body) are the 5 hazards with the highest in-degree value, and in-degree values are respectively 31, 29, 21, 21, and 21. These hazards all are material factors, indicating that material factors are prone to form armed hazards under the influence of dormant hazards.
Cumulative degree distribution of the I-FRPN is shown in Fig. 3. The cumulative degree distribution presents a power-law distribution that has the approximate fit P(k) = 3.7179x −1.285 ( R 2 = 0.8101 ). The above result deviates from the power-law nature for lager k, which indicates that the I-FRPN has scale-free property 18,37 . It means that a few hub nodes play a dominant role in the I-FRPN. If we can find these key nodes, the spread of risk can be slowed down or even blocked, thus preventing the occurrence of dam break. The degree studied in this section is an important indicator for judging the importance of network nodes. In addition, there are also  www.nature.com/scientificreports/ indicators such as betweenness centrality and closeness centrality that are also commonly used to measure the importance of nodes. In the next section, we will conduct more analysis on this aspect.
Network diameter and average path length. The network diameter, also known as the maximum path length of a network, represents the largest step length between two nodes in the network 34 . After calculation, the network diameter of the I-FRPN is 8, which means that a hazard node can affect any node in the network only after a maximum of 8 steps. The most distant node pairs of the network are v32 and v150 or v7 and v45. Compared with some accident networks studied in the past 15,37,38 , the diameter of I-FRPN is larger, and the evolution path of the risk is complicated. The characteristic path length is also called the average path length. After calculation, the average path length of the I-FRPN is 2.81, indicating that it takes less than 3 steps on average to transfer the risk of dam break from one hazard to another hazard. The above results show that the characteristic path length of the I-FRPN is small, and the risk of dam break can be spread quickly on the network. If no corresponding measures are taken, the emergence of a serious hazard may cause a tailings dam break in a relatively short time.
Clustering coefficient and small-world property. The clustering coefficient of the I-FRPN refers to the degree of interconnection between adjacent nodes of a hazard node in the network 37 . That is to say, there is no clustering coefficient for nodes with a degree value of 1. In this paper, the average clustering coefficient of the I-FRPN is calculated by Pajek software as 0.15. After excluding the nodes with a degree of 1, the clustering coefficients of the hazard nodes in the network are obtained, as shown in Fig. 4. It can be seen from the figure that the clustering coefficient of the hazard node in the I-FRPN is between 0 and 0.5. The clustering coefficients of hazard 32 (Insufficient tank length) and 220 (The maximum flow rate of flood control structure design is greater than the allowable flow rate of building materials) are both 0.5, which are the nodes with the largest clustering coefficient, indicating that the adjacent hazards of the hazard 32 and 220 have a strong correlation and show strong clustering.
Small-world networks usually have large clustering coefficients and small characteristic path lengths 34 . In order to judge whether the clustering coefficient of the I-FRPN meets the requirements of the small world, this paper constructs a random network with the same number of nodes and the same degree value as the I-FRPN, and calculates the clustering coefficient to be 0.08, which is smaller than the clustering coefficient of the I-FRPN (0.15). The equal-sized dam failure risk random network is called the mode of WW, as shown in Fig. 5. Combined with the characteristic path length of the I-FRPN is only 2.81, it can be concluded that the I-FRPN has smallworld property. In other words, the break accident for Dam I has the characteristics of multi-factor coupling and short disaster path.
Key hazards nodes in the I-FRPN. The paper first treats(deletes) the node with the largest index value and calculates the network efficiency, and then calculates the network efficiency after every 5 hazard nodes are treated. Figure 6 shows the changes of the network efficiency under the different hazard remediation methods.
In Fig. 6, it can be found that the preferential treatment of nodes with large betweenness centrality can achieve better results in the early stage (low deleting proportion). In other words, when the remediation proportion of hazard nodes is small, the risk propagation speed can be reduced more quickly by the betweenness centrality. However, when the proportion of hazard remediation reaches 13.68%, the hazard node with a higher degree value will have a better effect of reducing risk spread.  www.nature.com/scientificreports/ It can be seen from Fig. 6 that the MCHRM performs better than the other three commonly used methods, whether in the early stage of the hazard node remediation or in other stages. In addition, we can also find that all four methods show that when the proportion of node remediation reaches about 30%, the decline in network efficiency tends to slow down significantly. Further increasing the proportion of node remediation will not significantly reduce the propagation efficiency of the network. In other words, when we are in the process of hazard remediation of tailings dams, if we give priority to the top 30% of hazard nodes determined by the MCHRM, we can use the vulnerability of the network to reduce network efficiency more quickly. In this paper, these hazard nodes that can quickly reduce the propagation efficiency of the I-FRPN are called key hazards of Dam I failure, and the relationships between these key hazards are called the key propagation paths.
Failure process of Feijão Dam I. Since the weights between nodes in I-FRPN are assumed to be equal, only relying on network centrality analysis may miss the key hazards of Dam I failure. In order to overcome the problem, the paper has expanded the selection range of key hazards and set the key hazards as the top 45% of www.nature.com/scientificreports/ the index value. The I-FRPN has a total of 117 hazard nodes, and the top 45% of the index value includes 53 nodes. The expanded key hazards determined by MCHRM are shown in Table 1. The first column of Table 1 is the serial number of the key hazards, indicating the importance of the hazards. The third column is the name of the hazard to be studied, the second column is the number (ID) of the hazard, the sixth column is the level of the corresponding hazard node, and the fourth and fifth columns are the degree value and the betweenness centrality of the hazard node. By consulting the monitoring data, daily inspection results and safety evaluation information of each hazard before the failure of Dam I, the level of each hazard is obtained according to the grading standards of hazard indicators in "Appendix B", as shown in Table 1.
By excluding the hazard nodes of level 1 in the normal state, we can determine that there are 30 key hazards in the failure accident of Feijão Dam I. Combining the evolution relationship among the hazards based on evidence in "Appendix A", we can obtain the 240 propagation paths between key hazards. The key hazards and propagation paths of Dam I failure are shown in Fig. 7.

Comparison and analysis
To verify whether the key hazards (causes) of the Dam I failure identified are reasonable, this paper compares the above results with the conclusions made by the accident investigation expert group chaired by Dr. Peter K. Robertson. The expert group concluded that the direct cause of the failure of the Dam I was the tailings liquefaction of the dam. The expert group conducted research on the composition of the dam body material and the dam-break trigger mechanism, and found that 6 technical problems were the main causes leading to the dam break. Compare the key hazards with a level greater than 1 in Table 2 with the main causes found by the expert group 36 , as shown in Table 2.
Through comparison, it can be found that the main causes of the Dam I failure proposed by the expert group are 6 aspects, involving 8 hazard nodes. When the key hazards identified by the MCHRM are used as the priority remediation criteria (top 30%), the hazard 5, 70, 167, 195, and 200 are consistent with the causes of the dam failure mentioned in the expert group's conclusion, accounting for 62.5% of the 8 hazards; when the priority remediation range is increased to the top 45%, hazard 47, 77 and 82 are also included.
The above comparison results show that the MCHRM can better find the key causes of the dam failure. When the priority remediation range is increased by 15%, it will be possible to cover all the main causes. Although the conclusions of the expert group cannot be completely equated with the true causes and risk propagation paths of Dam I failure, the expert group members have rich experience and outstanding academic attainments on the issue of tailing dam failure. Therefore, expert group's conclusion is highly reliable. In addition, the failure causes and risk propagation paths of the Dam I identified in the paper also involve some hazards and propagation paths that the expert group did not mention, which may include some problems that the expert group did not notice, so it will help improve the safety management of tailings dams.

Discussion
The research content of the paper mainly includes hazard identification, the construction of the propagation network of tailings dam failure risk (PNTDFR), the analysis of the law of risk evolution, the identification of key hazards of tailings dam failure, and the characterization of the accident formation process. A flow chart showing the full-text research methods and results is shown in Fig. 8.
The paper analyzes the laws and regulations, technical specifications and procedures related to tailings dams one by one, and refers to relevant scientific and technological literature, accident cases and other supplementary evidence, to identify the hazards that may exist in the different life cycle stages of the tailings dam system. The method is called a three-dimensional hazard identification framework (THIF). This method not only avoids the omission of hazards, but is also more objective than the subjective identification methods in the past.
Compared with commonly used methods such as accident trees and accident chains, complex networks can more completely and systematically link these evidence-based hazards, and characterize the evolution process of dam-break risk in the form of a network. In addition, through the analysis of the network characteristics of I-FRPN, it is found that the propagation of dam-break risk presents a small-world and scale-free nature, while the distribution of hazards shows clustering features. The above characteristics have not been discovered in the conventional failure analysis of tailings dams.
In the determination of key hazards, we can see from Fig. 6 that the commonly used degree centrality, betweenness centrality, and close centrality can all indicate the importance of the hazard node to a certain extent, because the network efficiency all showed a rapid decline after hazard nodes with big indicator value are deleted. The hazards with greater betweenness centrality bear more risk propagation tasks, while the closeness centrality of hazards reflects its connection with other hazards. The two centrality indicators reflect the importance of hazards from different points. The MCHRM not only utilizes the advantages of the three indicators, but also combines the characteristics of multi-stage propagation of dam-break risk, which better reflects the importance of hazards of dam-break. For the problem of hazard remediation, the importance of hazards determined by MCHRM also represents the best order of hazard remediation.
The MCHRM can significantly reduce the network efficiency, but there are also the problems that the severity or level of the hazards is not considered, and the weights between nodes in the network are assumed to be equal, which will lead to a certain difference between identified key hazards and real key hazards from tailings dam failure. At the same time, due to the complex causes of dam failure accidents and the difficulty of quantification, it is difficult to accurately give the weight of the relationship between hazards. In order to solve the above problems, this paper sets a certain reserve range when determining the range of key nodes in the PNTDFR,  Figure 7. Key hazards and propagation paths of Dam I failure. www.nature.com/scientificreports/ that is, increases the range of priority remediation. The specific reserve range can be adjusted to a certain extent according to the difference of the research objects. Key hazards are the main causes of dam failure, but for a specific accident, not all key hazards have played an important role. Therefore, if you want to reproduce the process of the accident, you must determine the status of these key hazards in the risk evolution of the accident. The network constituted by key hazards in the trigger state and the relationship between hazards intuitively represents the whole process of the accident.
Although this paper has done a lot of work to find the key hazards and characterize the accident formation process, there are still three shortcomings: a. Although the reserve range of priority remediation can cover all key hazards of dam failure, it is difficult to give an accurate reserve ratio, and the actual application needs to combine the experience of some technical personnel. b. In the formulation of hazard grading standards, due to the numerous influencing factors of hazards and the difficulty of quantifying some of the influencing factors, the grading standards of some hazards adopt a subjective qualitative classification method, which affects the accuracy of some grading indicators. c. The hazards and the relationships between hazards in this paper are all based on evidence (accident cases, laws and regulations, documents and media, etc.), but the reliability of different evidences is different, which will affect the accuracy of the research. To better solve the above problems and improve the practicability of above methods, the author of this paper plans to study more accident cases in the next step, so as to determine a more specific reserve range of priority remediation and build a hazard information database of tailings dams, which are suitable for the whole industry. At the same time, the paper will consider the evidence according to the reliability of the evidence, and select more quantitative indicators to classify the hazard indicators to improve the practicability of the methods.

Conclusion
The paper proposes an identification method: a three-dimensional hazard identification framework (THIF), which can identify the hazards of tailings dam accidents in a more systematic, complete and objective manner. Applying it to Dam I, based on the life cycle stage, dam structure, surrounding environment, personnel composition, and management system of the tailings dam, it is found that there may be 117 hazards and 535 relationships between hazards in this tailings dam. Based on the identified hazards and the relationship between hazards, this paper uses hazards to represent nodes and the relationship between hazards to represent edges, and constructs an I-FRPN that characterizes the propagation process of Dam I failure risk. Through the analysis of characteristics, it is found that the propagation of the failure risk of Dam I presents a small-world and scale-free effect.
By absorbing the advantages of betweenness centrality and degree centrality under different remediation proportion of hazard nodes in finding key hazard nodes, the paper proposes the MCHRM to identify the key hazards and the priority remediation order among the key hazards combined with the three-layer and two-stage characteristics of the PNTDFR. By analyzing the I-FRPN, it can be found that when the priority remediation range is increased from 30 to 45%, the key hazards obtained by the MCHRM will cover all the causes of accidents proposed by the Dam I failure investigation expert group. At the same time, the paper compares the monitoring data, daily inspection results and safety evaluation information of key hazards with the "Grading standards of hazard indicators", confirms that 30 key hazards are in trigger state, and obtains the formation process of the Dam I failure.